/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.payments.provider;
import static org.testng.AssertJUnit.assertEquals;
import org.testng.annotations.Test;
import org.threeten.bp.ZonedDateTime;
import cern.jet.random.engine.MersenneTwister;
import com.opengamma.analytics.financial.instrument.index.IborIndex;
import com.opengamma.analytics.financial.instrument.payment.CapFloorIborDefinition;
import com.opengamma.analytics.financial.interestrate.payments.derivative.CapFloorIbor;
import com.opengamma.analytics.financial.model.interestrate.HullWhiteOneFactorPiecewiseConstantInterestRateModel;
import com.opengamma.analytics.financial.model.interestrate.definition.HullWhiteOneFactorPiecewiseConstantParameters;
import com.opengamma.analytics.financial.montecarlo.provider.HullWhiteMonteCarloMethod;
import com.opengamma.analytics.financial.provider.calculator.hullwhite.PresentValueCurveSensitivityHullWhiteCalculator;
import com.opengamma.analytics.financial.provider.calculator.hullwhite.PresentValueHullWhiteCalculator;
import com.opengamma.analytics.financial.provider.description.HullWhiteDataSets;
import com.opengamma.analytics.financial.provider.description.MulticurveProviderDiscountDataSets;
import com.opengamma.analytics.financial.provider.description.interestrate.HullWhiteOneFactorProviderDiscount;
import com.opengamma.analytics.financial.provider.description.interestrate.HullWhiteOneFactorProviderInterface;
import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderDiscount;
import com.opengamma.analytics.financial.provider.sensitivity.hullwhite.ParameterSensitivityHullWhiteDiscountInterpolatedFDCalculator;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MultipleCurrencyParameterSensitivity;
import com.opengamma.analytics.financial.provider.sensitivity.parameter.ParameterSensitivityParameterCalculator;
import com.opengamma.analytics.financial.util.AssertSensitivityObjects;
import com.opengamma.analytics.math.random.NormalRandomNumberGenerator;
import com.opengamma.analytics.math.statistics.distribution.NormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
import com.opengamma.financial.convention.calendar.Calendar;
import com.opengamma.util.money.Currency;
import com.opengamma.util.money.MultipleCurrencyAmount;
import com.opengamma.util.test.TestGroup;
import com.opengamma.util.time.DateUtils;
/**
* Tests on the Hull-White one factor method to price Cap/Floor on Ibor.
*/
@Test(groups = TestGroup.UNIT)
public class CapFloorIborHullWhiteMethodTest {
private static final MulticurveProviderDiscount MULTICURVES = MulticurveProviderDiscountDataSets.createMulticurveEurUsd();
private static final HullWhiteOneFactorPiecewiseConstantParameters HW_PARAMETERS = HullWhiteDataSets.createHullWhiteParameters();
private static final IborIndex EURIBOR3M = MulticurveProviderDiscountDataSets.getIndexesIborMulticurveEurUsd()[0];
private static final Currency EUR = EURIBOR3M.getCurrency();
private static final Calendar CALENDAR = MulticurveProviderDiscountDataSets.getEURCalendar();
private static final HullWhiteOneFactorProviderDiscount HW_MULTICURVES = new HullWhiteOneFactorProviderDiscount(MULTICURVES, HW_PARAMETERS, EUR);
// Cap/floor description
private static final ZonedDateTime FIXING_DATE = DateUtils.getUTCDate(2011, 1, 3);
private static final double NOTIONAL = 100000000; //100m
private static final double STRIKE = 0.02;
private static final boolean IS_CAP = true;
private static final CapFloorIborDefinition CAP_LONG_DEFINITION = CapFloorIborDefinition.from(NOTIONAL, FIXING_DATE, EURIBOR3M, STRIKE, IS_CAP, CALENDAR);
private static final CapFloorIborDefinition CAP_SHORT_DEFINITION = CapFloorIborDefinition.from(-NOTIONAL, FIXING_DATE, EURIBOR3M, STRIKE, IS_CAP, CALENDAR);
private static final CapFloorIborDefinition PUT_LONG_DEFINITION = CapFloorIborDefinition.from(NOTIONAL, FIXING_DATE, EURIBOR3M, STRIKE, !IS_CAP, CALENDAR);
// To derivative
private static final ZonedDateTime REFERENCE_DATE = DateUtils.getUTCDate(2008, 8, 18);
private static final CapFloorIbor CAP_LONG = (CapFloorIbor) CAP_LONG_DEFINITION.toDerivative(REFERENCE_DATE);
private static final CapFloorIbor CAP_SHORT = (CapFloorIbor) CAP_SHORT_DEFINITION.toDerivative(REFERENCE_DATE);
private static final CapFloorIbor PUT_LONG = (CapFloorIbor) PUT_LONG_DEFINITION.toDerivative(REFERENCE_DATE);
private static final CapFloorIborHullWhiteMethod METHOD_HW = CapFloorIborHullWhiteMethod.getInstance();
private static final HullWhiteOneFactorPiecewiseConstantInterestRateModel MODEL = new HullWhiteOneFactorPiecewiseConstantInterestRateModel();
private static final PresentValueHullWhiteCalculator PVHWC = PresentValueHullWhiteCalculator.getInstance();
private static final PresentValueCurveSensitivityHullWhiteCalculator PVCSHWC = PresentValueCurveSensitivityHullWhiteCalculator.getInstance();
private static final double SHIFT = 1.0E-6;
private static final ParameterSensitivityParameterCalculator<HullWhiteOneFactorProviderInterface> PS_HW_C = new ParameterSensitivityParameterCalculator<>(PVCSHWC);
private static final ParameterSensitivityHullWhiteDiscountInterpolatedFDCalculator PS_HW_FDC = new ParameterSensitivityHullWhiteDiscountInterpolatedFDCalculator(PVHWC, SHIFT);
private static final int NB_PATH = 12500;
private static final double TOLERANCE_PV = 1.0E-2;
private static final double TOLERANCE_PV_DELTA = 1.0E+0; // 0.01 currency unit for 1bp
@Test
public void presentValueStandard() {
final double tp = CAP_LONG.getPaymentTime();
final double t0 = CAP_LONG.getFixingPeriodStartTime();
final double t1 = CAP_LONG.getFixingPeriodEndTime();
final double theta = CAP_LONG.getFixingTime();
final double deltaF = CAP_LONG.getFixingAccrualFactor();
final double deltaP = CAP_LONG.getPaymentYearFraction();
final double alpha0 = MODEL.alpha(HW_PARAMETERS, 0.0, theta, tp, t0);
final double alpha1 = MODEL.alpha(HW_PARAMETERS, 0.0, theta, tp, t1);
final double ptp = MULTICURVES.getDiscountFactor(EUR, tp);
final double forward = MULTICURVES.getSimplyCompoundForwardRate(EURIBOR3M, t0, t1, CAP_LONG.getFixingAccrualFactor());
double kappa = Math.log((1.0 + deltaF * STRIKE) / (1.0 + deltaF * forward));
kappa += -(alpha1 * alpha1 - alpha0 * alpha0) / 2.0;
kappa /= alpha1 - alpha0;
final ProbabilityDistribution<Double> normal = new NormalDistribution(0, 1);
double priceExpected = (1.0 + deltaF * forward) * normal.getCDF(-kappa - alpha0) - (1.0 + deltaF * STRIKE) * normal.getCDF(-kappa - alpha1);
priceExpected *= deltaP / deltaF * ptp;
priceExpected *= NOTIONAL;
final MultipleCurrencyAmount priceMethod = METHOD_HW.presentValue(CAP_LONG, HW_MULTICURVES);
assertEquals("Cap/floor: Hull-White pricing", priceExpected, priceMethod.getAmount(EUR), TOLERANCE_PV);
}
//TODO: present value in arrears
@Test
public void presentValueLongShort() {
final MultipleCurrencyAmount priceLong = METHOD_HW.presentValue(CAP_LONG, HW_MULTICURVES);
final MultipleCurrencyAmount priceShort = METHOD_HW.presentValue(CAP_SHORT, HW_MULTICURVES);
assertEquals("Cap/floor: Hull-White pricing", priceLong.getAmount(EUR), -priceShort.getAmount(EUR), TOLERANCE_PV);
}
@Test
/**
* Tests present value curve sensitivity when the valuation date is on trade date.
*/
public void presentValueCurveSensitivity() {
final MultipleCurrencyParameterSensitivity pvpsExact = PS_HW_C.calculateSensitivity(CAP_LONG, HW_MULTICURVES, HW_MULTICURVES.getMulticurveProvider().getAllNames());
final MultipleCurrencyParameterSensitivity pvpsFD = PS_HW_FDC.calculateSensitivity(CAP_LONG, HW_MULTICURVES);
AssertSensitivityObjects.assertEquals("SwaptionPhysicalFixedIborSABRMethod: presentValueCurveSensitivity ", pvpsExact, pvpsFD, TOLERANCE_PV_DELTA);
}
@Test
/**
* Tests the Hull-White parameters sensitivity.
*/
public void presentValueHullWhiteSensitivity() {
presentValueHullWhiteSensitivityInstrument(CAP_LONG);
presentValueHullWhiteSensitivityInstrument(CAP_SHORT);
presentValueHullWhiteSensitivityInstrument(PUT_LONG);
}
private void presentValueHullWhiteSensitivityInstrument(final CapFloorIbor instrument) {
final double[] hwSensitivity = METHOD_HW.presentValueHullWhiteSensitivity(instrument, HW_MULTICURVES);
final int nbVolatility = HW_PARAMETERS.getVolatility().length;
final double shiftVol = 1.0E-6;
final double[] volatilityBumped = new double[nbVolatility];
System.arraycopy(HW_PARAMETERS.getVolatility(), 0, volatilityBumped, 0, nbVolatility);
final double[] volatilityTime = new double[nbVolatility - 1];
System.arraycopy(HW_PARAMETERS.getVolatilityTime(), 1, volatilityTime, 0, nbVolatility - 1);
final double[] pvBumpedPlus = new double[nbVolatility];
final double[] pvBumpedMinus = new double[nbVolatility];
final HullWhiteOneFactorPiecewiseConstantParameters parametersBumped = new HullWhiteOneFactorPiecewiseConstantParameters(HW_PARAMETERS.getMeanReversion(), volatilityBumped, volatilityTime);
final HullWhiteOneFactorProviderDiscount bundleBumped = new HullWhiteOneFactorProviderDiscount(MULTICURVES, parametersBumped, EUR);
final double[] hwSensitivityExpected = new double[hwSensitivity.length];
for (int loopvol = 0; loopvol < nbVolatility; loopvol++) {
volatilityBumped[loopvol] += shiftVol;
parametersBumped.setVolatility(volatilityBumped);
pvBumpedPlus[loopvol] = METHOD_HW.presentValue(instrument, bundleBumped).getAmount(EUR);
volatilityBumped[loopvol] -= 2 * shiftVol;
parametersBumped.setVolatility(volatilityBumped);
pvBumpedMinus[loopvol] = METHOD_HW.presentValue(instrument, bundleBumped).getAmount(EUR);
hwSensitivityExpected[loopvol] = (pvBumpedPlus[loopvol] - pvBumpedMinus[loopvol]) / (2 * shiftVol);
assertEquals("Cap/floor Ibor - Hull-White sensitivity adjoint: derivative " + loopvol + " - difference:" + (hwSensitivityExpected[loopvol] - hwSensitivity[loopvol]),
hwSensitivityExpected[loopvol], hwSensitivity[loopvol], 1.0E-0);
volatilityBumped[loopvol] = HW_PARAMETERS.getVolatility()[loopvol];
}
}
@Test(enabled = true)
/**
* Compare explicit formula with Monte-Carlo and long/short and payer/receiver parities.
*/
public void monteCarlo() {
HullWhiteMonteCarloMethod methodMC;
methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), 10 * NB_PATH);
// Seed fixed to the DEFAULT_SEED for testing purposes.
final MultipleCurrencyAmount pvExplicit = METHOD_HW.presentValue(CAP_LONG, HW_MULTICURVES);
final MultipleCurrencyAmount pvMC = methodMC.presentValue(CAP_LONG, EUR, HW_MULTICURVES);
assertEquals("Cap/floor - Hull-White - Monte Carlo", pvExplicit.getAmount(EUR), pvMC.getAmount(EUR), 5.0E+2);
final double pvMCPreviousRun = 136707.032;
assertEquals("Swaption physical - Hull-White - Monte Carlo", pvMCPreviousRun, pvMC.getAmount(EUR), TOLERANCE_PV);
methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), 10 * NB_PATH);
final MultipleCurrencyAmount pvShortMC = methodMC.presentValue(CAP_SHORT, EUR, HW_MULTICURVES);
assertEquals("Swaption physical - Hull-White - Monte Carlo", -pvMC.getAmount(EUR), pvShortMC.getAmount(EUR), TOLERANCE_PV);
}
@Test(enabled = false)
/**
* Performance for a high number of paths.
*/
public void performance() {
long startTime, endTime;
final MultipleCurrencyAmount pvExplicit = METHOD_HW.presentValue(CAP_LONG, HW_MULTICURVES);
HullWhiteMonteCarloMethod methodMC;
final int nbPath = 1000000;
methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);
final int nbTest = 10;
final double[] pv = new double[nbTest];
final double[] pvDiff = new double[nbTest];
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pv[looptest] = methodMC.presentValue(CAP_LONG, EUR, HW_MULTICURVES).getAmount(EUR);
pvDiff[looptest] = pv[looptest] - pvExplicit.getAmount(EUR);
}
endTime = System.currentTimeMillis();
System.out.println(nbTest + " pv cap/floor Hull-White MC method (" + nbPath + " paths): " + (endTime - startTime) + " ms. Error: " + pvDiff[0]);
// Performance note: price: 12-Jun-12: On Mac Pro 3.2 GHz Quad-Core Intel Xeon: 2400 ms for 10 cap with 1,000,000 paths.
}
}